A spring with spring constant k = 12 slug/s2 has a mass attached that stretches the spring 2-2/3 ft. The damping coefficient is 7 slug/s. The mass is pushed 1 ft above the rest position and then released with a velocity of 1 ft/s downward. set up the differential equation that describes the motion under the assumption of this section. Solve the differential equation. State whether the motion of the spring system is harmonic, damped oscillation, critically damped oscillation, or overdamped. If the motion is overdamped oscillation, rewrite in the amplitude-phase form

A spring with spring constant k = 12 slug/s2 has a mass attached that stretches the spring 2-2/3 ft. The damping coefficient is 7 slug/s. The mass is pushed 1 ft above the rest position and then released with a velocity of 1 ft/s downward. set up the differential equation that describes the motion under the assumption of this section. Solve the differential equation. State whether the motion of the spring system is harmonic, damped oscillation, critically damped oscillation, or overdamped. If the motion is overdamped oscillation, rewrite in the amplitude-phase form